How is gas release rate calculated?
The release rate is the source term for every downstream consequence calculation. For a gas leaking from pressurised equipment it is calculated from compressible orifice flow, using either the choked (sonic) expression or the subsonic expression depending on the ratio of ambient to stagnation pressure.
Choked versus subsonic flow
As pressure in a vessel rises, the velocity at the hole increases until it reaches the speed of sound. Beyond that point the flow is choked and further increases in upstream pressure raise the mass flow only through density, not velocity. The boundary is the critical pressure ratio, which depends on the ratio of specific heats and is around 0.53 for typical hydrocarbon gases.
In other words, any hydrocarbon system above roughly 2 bara absolute will discharge in the choked regime at the start of the release.
The inputs that actually control the answer
- Hole area — the rate scales with the square of hole diameter, so hole-size selection dominates the result.
- Stagnation pressure — the rate scales roughly linearly in the choked regime.
- Discharge coefficient — around 0.61 to 0.62 for a sharp-edged hole, higher for rounded nozzles and full-bore breaks.
- Molar mass and temperature — heavier and colder gas gives a higher mass rate for the same conditions.
- Compressibility factor — at high pressure, ideal-gas treatment can overstate the rate noticeably.
Steady rate or decaying rate?
A conservative screening study may hold the initial rate constant for the release duration. A realistic study integrates the inventory: as gas leaves, the vessel pressure falls, the rate falls, and eventually the flow drops out of the choked regime. For isolatable sections with modest inventory the difference between the two treatments is large, and the constant-rate assumption can overstate the released mass by a wide margin.
Duration matters as much as rate. A high rate that lasts ten seconds may be less onerous for toxic dose than a modest rate that runs until manual isolation.
Liquid and two-phase releases
For a subcooled liquid the Bernoulli orifice equation applies. For a liquid stored above its atmospheric boiling point the release flashes at the orifice and a two-phase treatment is required; using a gas-only or liquid-only equation there gives the wrong rate and the wrong post-release physics.
Frequently asked questions
What hole sizes should be assessed?
Standard QRA practice uses representative bands, commonly a small (about 5 mm), medium (about 25 mm), large (about 100 mm) and full-bore rupture case, each with its own leak frequency.
Does temperature affect the release rate?
Yes. Mass rate varies inversely with the square root of absolute stagnation temperature, so a cold release is heavier for the same pressure — and the cold jet is also more likely to behave as a dense gas.
Why does the calculated rate change when a real-gas model is used?
Because the compressibility factor Z appears under the square root in the denominator. At high pressure Z can be well below one, and ignoring it changes the calculated mass rate by several percent to tens of percent.
Calculators for this topic
- Gas Discharge — Gas discharge rate calculator for pressurised releases
- Two-Phase Blowdown — Two-phase blowdown and depressurisation calculator
- Gas Dispersion — Atmospheric gas dispersion calculator